Linear momentum: mass times velocity

5 minAS Level3.1.3

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can define linear momentum, calculate it with the right sign and unit, and find the change in momentum when something speeds up, slows down or bounces.

Key to the symbols

The main symbols used in this lesson:

Symbol	Meaning
$\Delta$	a change in, so $\Delta v$ means "the change in $v$ "

Which would you rather stop?

A cricket ball flying at you at $40\ \text{m s}^{-1}$ , or a car rolling towards you at walking pace? The car is slower, but it is far harder to stop. How hard something is to stop depends on its mass and its velocity, so physicists bundle the two together as momentum.

	mass / kg	velocity / m s⁻¹	momentum / kg m s⁻¹
cricket ball	0.16	40	6.4
rolling car	1000	0.50	500

(Please don't try to stop either.)

Definition

Linear momentum

Linear momentum is the product of an object's mass and its velocity:

$p = mv$

It is a vector, pointing the same way as the velocity. Its unit is $\text{kg m s}^{-1}$ , which is the same as $\text{N s}$ .

A vector, so signs matter

Choose a positive direction and stick to it. A $2.0\ \text{kg}$ trolley moving right at $3.0\ \text{m s}^{-1}$ has $p = +6.0\ \text{kg m s}^{-1}$ . The same trolley moving left at the same speed has $p = -6.0\ \text{kg m s}^{-1}$ . Same speed, opposite momentum.

Why is $\text{N s}$ the same as $\text{kg m s}^{-1}$ ? Because $1\ \text{N} = 1\ \text{kg m s}^{-2}$ , so $1\ \text{N s} = 1\ \text{kg m s}^{-1}$ . Force multiplied by time gives a change in momentum: a clue to the next lesson.

Quick check

CalculateQuestion 1 · Recall

Multiple choiceQuestion 2 · Recall

Answer the 2 questions above to continue.